Time is running out on the Knicks and their playoff chances, and a task that was already difficult is going to be nearly impossible without Carmelo Anthony playing at full strength.

New York had put together a desperation run as of late, winning 12 of its last 15 games before dropping a close one at home to the Wizards on Friday. The loss put them technically only one game out of the eighth spot in the East, but they trail Atlanta now by two games in the loss column.

Losing to Washington on one of the game’s final possessions isn’t a crime, as the Wizards are firmly in the postseason picture themselves. But it was disturbing in that New York largely played great, getting huge games from J.R. Smith and Amar’e Stoudemire.

The problem was Anthony, who finished with just 10 points and nine turnovers, likely due to attempting to play through an injured right shoulder.

X-rays on Anthony’s shoulder were negative, and the Knicks expect him to play Sunday at Miami. …

Anthony said he first suffered the injury during the Knicks’ win over the Brooklyn Nets on Wednesday night.

“Today was just the lingering effect on it,” said Anthony, who shot 5 of 14 from the field and missed all four of his 3-point attempts. “I just felt it just gave [out]. Throughout the course of the game, there was no strength in it — on the passes, causing turnovers, things like that. Hopefully, I’ll be all right.” …

“Well, I knew it was bothering him,” Knicks coach Mike Woodson said. “But you know, we’ve got to have Melo on the floor. … But it was bothering him. I knew that. He has nine turnovers, that’s not Carmelo.”

And that’s the issue right there.

The Knicks have to have Anthony on the floor, and have no shot at winning the last five games of the season — all of which are against Eastern Conference playoff teams, with the next one Sunday in Miami — with him performing the way he did against the Wizards.

It feels like time has run out on the Knicks and their playoff chances. Anthony gutting out the remainder of the season at less than 100 percent would make it official.

I don’t remember playing tonight. I didn’t play. Guys get a lot of money to be ready to play. No Knute Rockne speeches. It’s your job. If you’re a plumber and you don’t do your job, you don’t get any work. I don’t think a plumber needs a pep talk. If a doctor botches operations, he’s not a doctor anymore. If you’re a basketball player, you come ready. It’s called maturity. It’s your job.

Like it or not, motivation is part of an NBA coach’s job.

But that’s also precisely what Popovich is doing.

His credentials dwarf any other coach’s. He can play to his own ego and absolve himself of responsibility – and players will seek to please him. His years of success have earned him the ability to motivate this way, a method no other coach could use without alienating his team.

So, why not hold Motiejunas to what became a four-year, $31 million offer sheet once matched? Houston got something in return – a later trigger date on guaranteeing Motiejunas’ 2017-18 salary. Originally, that decision had to be made March 1 – which would’ve meant dropping Motiejunas from the team this season to prevent his salary from counting next season. Now, the Rockets can make that call in July, after this season is complete.

The following two Julys, Houston will also have a choice on guaranteeing Motiejunas’ upcoming salary or dropping him.

Essentially, Motiejunas is signing the most lucrative Hinkie Special in NBA history. If he plays well and stays healthy, the Rockets have Motiejunas at an affordable rate. If he struggles or his back injuries flare up, they can drop him with little to no penalty.

After they backed themselves into this corner, Motiejunas and his agent, B.J. Armstrong, didn’t do so bad. Considering the similarity between this contract and the Nets’ original offer sheet, it seems Houston helped Armstrong save face after a bungled free agency (which is easier to accept when you’re adding a talented reserve to a formidable team).

But for how little is guaranteed and how much control the Rockets hold over the next four years, wouldn’t Motiejunas have been better off accepting the $4,433,683 qualifying offer?

This means Motiejunas can’t sign with the Nets, who signed him to the original offer sheet, for one year.

I bet it also means Motiejunas and Houston have agreed to a new contract. Otherwise, why release him from the offer sheet? The Rockets would be giving up a tremendous amount of leverage out of the goodness of their hearts – unless this is just a prelude to a new deal with Houston.